Can there be a homogeneous system of two linear equations in

Can there be a homogeneous system of two linear equations in three unknowns which has a unique solution? Need an example

Solution

a system with fewer equation than unknowns has infinitely many solution. But it may also have no solution and such a system is known as undetermined system.

For example

x+3y-2z=5

3x+5y+6z=7

here we can solve by

x=-7z-1 and y=3z+2

where x and y are dependent variable

but we can have different choices for dependent variable

y=-3x\\7+11\\7 and z=-1\\7x and -1\\7